Though under non-linear accretion, all black holes in four and higher dimensions obey the weak Cosmic Censorship Conjecture, however they generally violate it for the linear test particle accretion with the exception of five dimensional rotating black hole with a single rotation. In dimension greater than five, there exists no extremal condition for black hole with single rotation and hence it can never be overspun. However it does exist for two rotations of five dimensional rotating black hole and then black hole could indeed be overspun under linear accretion. In this paper we study the case of six dimensional rotating black hole with two rotations and show that unlike the five dimensional black hole it cannot be overspun under linear accretion. We would conjecture that so should also be the case in all dimensions greater than six. Thus CCC may always be obeyed for rotating black hole in all dimensions greater than five.